Method and system for autonomous tracking of a mobile target by an unmanned aerial vehicle

ABSTRACT

A method and system for autonomous tracking of a mobile target such as a ground vehicle by an unmanned aerial vehicle are provided. The method and system utilize an approach that tracks a mobile ground target by using a ground vehicle model with an ummanned aerial vehicle model, with velocity and acceleration constraints. These real-world constraints ensure that the method is applicable to a general class of unmanned aerial vehicles and ground targets. One or more sensors are employed on the unmanned aerial vehicle, with the sensors having at least one field-of-view sensing cone over the ground. A position and path of the mobile target are monitored through input from the sensors on the unmanned aerial vehicle. The method and system detect and estimate the position and path of the mobile target when the target is inside the field-of-view sensing cone.

GOVERNMENT LICENSE RIGHTS

The U.S. Government may have certain rights in the present invention asprovided for by the terms of Contract No. F33615-01-C-1848 withAFRL/Wright Research Site.

BACKGROUND TECHNOLOGY

Unmanned aerial vehicles (UAVs) are remotely piloted or self-pilotedaircraft that can carry cameras, sensors, communications equipment, orother payloads. They have been used in a reconnaissance andintelligence-gathering role for many years. More recently, UAVs havebeen developed for the purpose of surveillance and target tracking.

Autonomous surveillance and target tracking performed by UAVs in eithermilitary or civilian environments is becoming an important aspect ofintelligence-gathering. However, tracking a moving target on the ground,such as a ground vehicle in motion on a road, with an unmanned aerialvehicle (UAV) presents various difficulties that need to be addressed inorder to have an effectively autonomous surveillance and target trackingsystem. For example, if there are minimum speed limits for the unmannedaerial vehicle, such as any fixed-wing UAV would have, the groundvehicle can easily give the slip to the tracking UAV. Another difficultythat needs to be addressed in a system for autonomous tracking of amoving target is the delay and noise inherent in visual recognition.

BRIEF DESCRIPTION OF THE DRAWINGS

Features of the present invention will become apparent to those skilledin the art from the following description with reference to thedrawings. Understanding that the drawings depict only typicalembodiments of the invention and are not therefore to be consideredlimiting in scope, the invention will be described with additionalspecificity and detail through the use of the accompanying drawings, inwhich:

FIG. 1 is a schematic diagram depicting a system for aerial tracking ofa ground vehicle according to one embodiment of the invention;

FIG. 2 is schematic overhead view depicting the path of a ground vehicleand the chase path covered by a hover-capable unmanned aerial vehicle inan urban setting;

FIG. 3 is a graph of the vertical motion above ground level (AGL) of thehover-capable unmanned aerial vehicle of FIG. 2; and

FIG. 4 is a schematic overhead view depicting the path of a groundvehicle and the chase path covered by a fixed-wing unmanned aerialvehicle in an urban setting.

DETAILED DESCRIPTION

In the following detailed description, embodiments are described insufficient detail to enable those skilled in the art to practice theinvention. It is to be understood that other embodiments may be utilizedwithout departing from the scope of the present invention. The followingdetailed description is, therefore, not to be taken in a limiting sense.

The present invention relates to a method and system for autonomoustracking of a mobile target, such as a ground motor vehicle, by anunmanned aerial vehicle (UAV). The method and system utilize an approachthat tracks a mobile ground target by using a ground vehicle model withan unmanned aerial vehicle model, with velocity and accelerationconstraints. These real-world constraints ensure that the method isapplicable to a general class of unmanned aerial vehicles and groundtargets.

In one approach of the present invention, the tracking of a mobiletarget is provided by using a ground vehicle model, comprising a twodimensional double integrator point mass model, with an unmanned aerialvehicle model comprising a three dimensional double integrator pointmass model, with velocity and acceleration constraints. Theseconstraints capture the capabilities of the real vehicle, therebyensuring that the method of the invention is applicable to any othervehicle model used. The point mass models capture typical vehiclemotion—indeed, an aircraft with closed loop attitude control andposition and velocity tracking control loops behaves like a threedimensional double integrator with position and velocity tracking timeconstants. A sensor model applicable to a wide range of sensors orsensor systems (giving target position and velocity though differentmeans such as vision, radar, or acoustics) can also be used.

It should be understood that the double integrator point mass modelsdescribed hereafter are merely a simplification of complex dynamicmodels for ground vehicles and unmanned aerial vehicles. Other modelsystems may also be employed to implement the present invention.

The present invention can be implemented by utilizing a computerhardware and/or software system, which provides a means for tracking amobile ground target by using a ground vehicle model with an unmannedaerial vehicle model, with velocity and acceleration constraints. Aposition and path of the mobile ground target are monitored throughinput from one or more sensors on the UAV, with the sensors having atleast one field-of-view (FOV) sensing cone over the ground. For example,several sensors can be employed by the UAV, giving several FOV cones ora much larger FOV cone. The system and method detect and estimate theposition and path of the mobile target when the target is inside thefield-of-view sensing cone.

A wide variety of sensors can be used in the UAV, such as visual, radar,acoustic, or laser radar (ladar) sensors. For example, a tracking cameracan be used in the UAV. The method and system of the invention alsoprovide for maintaining stable tracking even with extremely noisytracking sensors. The present invention is described in further detailhereafter.

Sensor Model

A camera sensor is modeled as being able to maintain target detectionwithin a right circular cone vertically beneath the UAV with the coneangle θ being equal to the field-of-view (FOV) angle α of the camera.Such an arrangement is illustrated in FIG. 1, which is a schematicdiagram depicting a system 100 for aerial tracking of a ground vehicle110 by a UAV 112 having at least one sensor 114. The UAV 112 can eitherbe a hover-capable aerial vehicle or a fixed-wing aerial vehicle. An FOVcone 118 projected by sensor 114 has an FOV circle 120 on the ground.The FOV circle 120 has a radius of z tan

$z\mspace{14mu}\tan\frac{\alpha}{2}$where z is the altitude of UAV 112.

Tracking control laws are described hereafter that are exponentiallystable and can maintain a stable tracking system even with extremelynoisy tracking sensors. The tracking system abstracts essential featuresof the tracking problem without the distractions of detailed UAVdynamics and various constraints. Furthermore, the present system easestracking design for UAVs whose attitude stabilization control laws(commonly known as the inner loop) are already implemented, andtherefore a given.

Chaser and Prey Models

Purely discretized models are used in the method of the invention as thehandling of delays is natural in this setting. However, analogousmethods call be developed for the continuous time setting, which is moreadvantageous if sensor noise characteristics are well known. In thiscase, a Kalman filter and Kalman predictor could be used to estimateprey vehicle motion (position, velocity and acceleration). The samplingtime is denoted with T, and x_(p), v_(p) denote planar position (x_(p),y_(p)) and velocity vectors of the prey (i.e., a mobile target such as aground vehicle), and x_(c), v_(c) denote the three dimensional position(x_(c), y_(c), z_(c)) and velocity vectors of the chaser (i.e., a UAV).The prey model is simply a double integrator with an unknownacceleration inputa_(p):x _(p)(k+1)=x _(p)(k)+Tv _(p)(k)v _(p)(k+1)=v _(p)(k)+Ta _(p)(k)where k=1, 2, 3 . . . is the sampling instant.The chaser model incorporates information about the position trackingand velocity tracking time constants (τ_(x) and τ_(v)) of the inner loopcontroller on board the UAV:

x_(c)(k + 1) = x_(c)(k) + Tv_(c)(k)${{v_{c}( {k + 1} )} = {{{- \frac{T}{\tau_{x}\tau_{v}}}{x_{c}(k)}} + {( {1 - \frac{T}{\tau_{v}}} ){v_{c}(k)}} + {\frac{T}{\tau_{x}\tau_{v}}x_{c}^{ref}}}},$where x_(c) ^(ref) is the current desired location of the chase vehicleto maintain tracking of the target vehicle. The next equation is for theplanar position error between the chaser and the prey. The planarcomponent of the vehicle position and velocity are denoted respectivelyby x_(c) ^(pl) and v_(c) ^(pl):

δ x_(pl) ≡ x_(c)^(pl) − x_(p) δ v_(pl) ≡ v_(c)^(pl) − v_(p)δ x_(pl)(k + 1) = δ x_(pl)(k) + T δ v_(pl)${{\delta\;{v_{pl}( {k + 1} )}} = \begin{matrix}{{{- \frac{T}{\tau_{x}\tau_{v}}}\delta\; x_{pl}} + {( {1 - \frac{T}{\tau_{v}}} )\delta\; v_{pl}} - {\frac{T}{\tau_{x}\tau_{v}}{x_{p}(k)}} -} \\{{\frac{T}{\tau_{v}}{v_{p}(k)}} - {{Ta}_{p}(k)} + {\frac{T}{\tau_{x}\tau_{v}}x_{c}^{{ref},{pl}}}}\end{matrix}},$where x_(c) ^(ref,pl) is the planar part of the chaser position setpoint.Tracking Control Law

If the tracking set point is set to cancel the terms arising from preyvehicle position, velocity, and acceleration in the error equationabove, there will be exponential tracking of the prey. The control lawin this case would be:x _(c) ^(ref,pl)(k)=x _(p)(k)+τ_(x) v _(p)(k)+τ_(x)τ_(v) a _(p)(k)However, it is necessary to work from delayed and noisy measurements ofthe prey position and velocity. To this end, estimates are made of thecurrent prey position, velocity, and acceleration from the measurements.It is assumed that the delay (nT) is an integral multiple of thesampling time T, which is realistic since the sampling time is smallcompared to the delay. The measurements are:x _(p) ^(meas)(k)=x _(p)(k−n)+v ₁v _(p) ^(meas)(k)=v _(p)(k−n)+v ₂.where v₁ and v₂ represent measurement noise, whose properties underdifferent operating conditions may be available. To estimate theacceleration driving the prey dynamics, a FIR (finite impulse response)filter has been developed. The filter simply takes a weighted average ofthe m past estimates of acceleration, assuming it to be constant overthat time period and giving maximum weight to the most recent estimate.

${\hat{a}}_{p} = {\frac{1}{T}{\sum\limits_{i = 1}^{m}{c_{i}( {{v_{p}^{meas}( {k - i + 1} )} - {v_{p}^{meas}( {k - i} )}} )}}}$${\sum\limits_{i = 1}^{m}c_{i}} = 1$While the number of past points used and filter coefficients used can bechosen to optimize some objective function, the following were chosen:m=5 and c₁= 17/32, c₂=¼, c₃=⅛, c₄= 1/16, c₅= 1/32. Using the estimate ofthe acceleration, prediction of the current state of the prey (positionand velocity) can be performed using the prey double integrator model:

${{\begin{pmatrix}{\hat{x}}_{p} \\{\hat{v}}_{p}\end{pmatrix}(k)} = {{{A^{m}\begin{pmatrix}{\hat{x}}_{p} \\{\hat{v}}_{p}\end{pmatrix}}( {k - m} )} + {\sum\limits_{i = 1}^{m - 1}{A^{i}b\;{\hat{a}}_{p}}}}},{{{where}\mspace{14mu} A} = \begin{pmatrix}I_{2} & {TI}_{2} \\0 & I_{2}\end{pmatrix}},{b = \begin{pmatrix}0 \\{TI}_{2}\end{pmatrix}}$and I₂ is the 2×2 identity matrix. It should be noted that the FIRfilter is used to account for general or unknown noise characteristics.If noise characteristics are known, optimal filters, such as discreteFIR, discrete Kalman filters, or continuous Kalman filters andpredictors can be used.

Finally, the vertical coordinate of the unmanned aerial vehicle isupdated with the following gradient descent type law that minimizes thecost function:

$J = {2\frac{{{\delta\; x_{pl}}}^{2}}{z_{c}^{2}\tan^{2}\frac{\alpha}{2}}}$with respect to z_(c), giving

${\overset{.}{z}}_{c} = {{{- \gamma}\frac{\partial J}{\partial z_{c}}} = {4\gamma\frac{{{\delta\; x_{pl}}}^{2}}{z_{c}^{3}\tan^{2}\frac{\alpha}{2}}}}$where γ is the gain of the gradient scheme (in units of distance²/time).The above cost function is motivated by the idea of maintaining theposition of the unmanned aerial vehicle and therefore its trackingcamera, within a square inscribed inside the field-of-view circle on theground.

The following examples are given to illustrate the present invention,and are not intended to limit the scope of the invention.

EXAMPLES

Simulations were performed with the above control law on arepresentation of a typical military operations urban terrain (MOUT)with both a hover-capable chaser UAV and a fixed-wing chaser UAV. Thefixed-wing chaser cannot go slower than a minimum velocity. The UAVcapabilities were as follows: maximum speeds of 25 m/s (hover-capable)and 40 m/s (fixed-wing), maximum acceleration of 10 m/s², τ_(x)=0.25 s,τ_(v)=0.5 s, the minimum speed for the fixed-wing vehicle was 25 m/s,and the vehicle flew between 25 m and 50 m above ground level (AGL). Thefield-of-view of the camera was taken as α=120°.

FIGS. 2 and 4 are schematic overhead map views depicting the chase pathresults for the hover-capable and fixed-wing UAVs, respectively. Theinstantaneous target vehicle (prey) position in each case is denoted bysolid circles at times of 1, 2, 3, 7, 14, 21, and 28 seconds (movingfrom left to right on the maps in FIGS. 2 and 4). The corresponding UAV(chaser) position is represented by an open circle at those same times.The path of the target vehicle is represented by a continuous solid lineand the path of the UAV is represented by a dotted line. The targetvehicle is always either accelerating or decelerating at 3 m/s². Thetarget vehicle has a maximum velocity of 25 m/s (almost 60 mph) and itnegotiates turns with a velocity of 7.5 m/s. The measurement noisevariance for both position and velocity is 5 units (very large comparedto actual values).

While FIG. 2 depicts the chase path covered by the hover-capable UAV,FIG. 3 is a graph of the vertical motion of the hover-capable UAV,showing the variation of the UAV's altitude AGL during the chase. Inthis case, the UAV chaser is able to maintain its prey in view whilefollowing the prey. The altitude remains in a small range, which isdesirable since UAV actuation authority should not be wasted in alteringaltitude except when necessary.

As shown in FIG. 4, the chase path covered by the fixed-wing UAVincludes figure-eights and circles around the prey as the prey slowsdown at the turns. Such a path is required since the fixed-wing UAVcannot fly slower than 25 m/s.

The UAV chasers are locally exponentially stable by design, since the xand y position error equations are exponentially stable, and thegradient descent is also stable. It may be possible to determine astability region of the tracking in the presence of UAV constraintsusing Sum of Squares programming.¹ Performance in the presence of noiseand occlusions, with no measurement for a few time steps, is alsoamenable to analysis in the Stun of Squares framework. ¹ See S. Prajnaet al., SOSTOOLS: Sum of squares optimization toolbox for MATLAB,available from http://www.cds.caltech.edu/sostools, andhttp://www.mit.edu/˜parillo/sostools, 2004.

Instructions for carrying out the various methods, process tasks,calculations, control functions, and the generation of signals and otherdata used in the operation of the system and method are implemented, insome embodiments, in software programs, firmware or computer readableinstructions. These instructions are typically stored on any appropriatemedium used for storage of computer readable instructions such as floppydisks, conventional hard disks, CD-ROM, flash memory ROM, nonvolatileROM, RAM, and other like medium.

The present invention may be embodied in other specific forms withoutdeparting from its essential characteristics. The described embodimentsare to be considered in all respects only as illustrative and notrestrictive. The scope of the invention is therefore indicated by theappended claims rather than by the foregoing description. All changesthat come within the meaning and range of equivalency of the claims areto be embraced within their scope.

1. A method for autonomous tracking of a mobile ground target by anunmanned aerial vehicle, comprising: tracking the mobile ground targetby using a ground vehicle model with an unmanned aerial vehicle model,with velocity and acceleration constraints; and monitoring a positionand path of the mobile ground target through input from one or moresensors on the unmanned aerial vehicle, the sensors having at least onefield-of-view sensing cone over the ground.
 2. The method of claim 1,wherein the ground vehicle model comprises a two dimensional doubleintegrator point mass model.
 3. The method of claim 1, wherein theunmanned aerial vehicle model comprises a three dimensional doubleintegrator point mass model.
 4. The method of claim 1, whereinacceleration of the mobile ground target is estimated from a finiteimpulse response filter.
 5. The method of claim 1, wherein monitoringthe position and path of the mobile ground target depends upon themobile target being inside of the field-of-view sensing cone.
 6. Themethod of claim 1, wherein the one or more sensors comprise at least oneof a visual sensor, a radar sensor, an acoustic sensor, or a laser radarsensor.
 7. The method of claim 1, wherein the sensors having a pluralityof field-of-view sensing cones over the ground.
 8. The method of claim1, wherein the mobile ground target comprises a motor vehicle.
 9. Themethod of claim 1, wherein the unmanned aerial vehicle comprises ahover-capable aerial vehicle.
 10. The method of claim 1, wherein theunmanned aerial vehicle comprises a fixed-wing aerial vehicle.
 11. Asystem for autonomous tracking of a mobile ground target by an unmannedaerial vehicle, comprising: a computer configured to track the mobileground target by using a ground vehicle model with an unmanned aerialvehicle model, with velocity and acceleration constraints; and one ormore sensors on the unmanned aerial vehicle that have at least onefield-of-view sensing cone over the ground; wherein detection of aposition and path of the mobile ground target depends upon the mobiletarget being inside of the field-of-view sensing cone.
 12. The system ofclaim 11, wherein the ground vehicle model comprises a two dimensionaldouble integrator point mass model.
 13. The system of claim 11, whereinthe unmanned aerial vehicle model comprises a three dimensional doubleintegrator point mass model.
 14. The system of claim 11, whereinacceleration of the mobile ground target is estimated from a finiteimpulse response filter.
 15. The system of claim 11, wherein the one ormore sensors comprise at least one of a visual sensor, a radar sensor,an acoustic sensor, or a laser radar sensor.
 16. The system of claim 11,wherein the unmanned aerial vehicle comprises a hover-capable aerialvehicle.
 17. The system of claim 11, wherein the unmanned aerial vehiclecomprises a fixed-wing aerial vehicle.
 18. A computer program product,comprising: a computer readable medium having instructions operable tobe executed to implement a method for autonomous tracking of a mobileground target by an unmanned aerial vehicle, the method comprising:tracking the mobile ground target by using a ground vehicle model withan unmanned aerial vehicle model, with velocity and accelerationconstraints; and monitoring a position and path of the mobile groundtarget through input from one or more sensors on the unmanned aerialvehicle.
 19. The computer program product of claim 18, wherein theground vehicle model comprises a two dimensional double integrator pointmass model.
 20. The computer program product of claim 18, wherein theunmanned aerial vehicle model comprises a three dimensional doubleintegrator point mass model.